On the Uncertainty in X-Ray Cluster Mass Estimates from the Equation of Hydrostatic Equilibrium

We study the uncertainty in galaxy cluster mass estimates derived from X-ray data, assuming hydrostatic equilibrium for the intracluster gas. Using a Monte Carlo procedure, we generate a general class of mass models allowing very massive clusters. We then compute the corresponding temperature profiles through the equation of hydrostatic equilibrium and compare them to observational data for some clusters. We find several massive clusters that pass the observational constraints, with integrated masses varying over quite a wide range. The resulting accuracy of the mass estimates is rather poor, the uncertainties larger than what is generally claimed. Despite the fact that the mass profile can be exactly determined mathematically from the temperature and surface brightness profiles, we find that very accurate measurements of both quantities are required to determine the actual mass with moderate accuracy. We argue that the tight constraints on cluster masses previously obtained arise from the fact that a too restricted class of mass density profiles has been investigated so far, without serious physical justification. Applying our procedure to the Perseus and then to the Coma clusters, we find that an improvement of the observational constraints results in a quite modest improvement in the accuracy of the mass estimate. For Coma, using the best current available data, we end up with an uncertainty of a factor of 2 for the mass within the Abell radius. This uncertainty rapidly increases at further radius.